Directional Analysis of Fibre Processes Related to Boolean Models.
Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
Let (Xt) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define Ji as the integral between iΔn and (i + 1)Δn of Xs. We give an approximation of the law of (J0,...,Jn-1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δn = n-1 we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown...
Divergences of Gauss-Markov random fields with application to statistical inference
Efficiency and robustness control via distorted maximum likelihood estimation
Efficiency rate and local deficiency of Huber's location estimators and of the α-estimators.
The paper studies the problem of selecting an estimator with (approximately) minimal asymptotic variance. For every fixed contamination level there is usually just one such estimator in the considered family. Using the first and the second derivative of the asymptotic variance with respect to the parameter which parametrizes the family of estimators the paper gives two examples of how to select the estimator and gives an approximation to a loss which we suffer when we use the estimator with approximately...
Efficient robust estimation of time-series regression models
The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior...
Estimación de correlaciones utilizando envolturas convexas.
En el presente trabajo se realiza un estudio de la envoltura convexa de una muestra normal bivariante, analizando la distribución de la pendiente de sus aristas. En base a ello se propone un estimador del coeficiente de correlación de la población, investigando algunas propiedades del mismo.
Estimates for distributions of sums of random variables with subexponential distributions.
Estimates of reliability for the normal distribution
The minimum variance unbiased, the maximum likelihood, the Bayes, and the naive estimates of the reliability function of a normal distribution are studied. Their asymptotic normality is proved and asymptotic expansions for both the expectation and the mean squared error are derived. The estimates are then compared using the concept of deficiency. In the end an extensive Monte Carlo study of the estimates in small samples is given.
Estimating After Sequential Selection and Ranking.
Estimation asymptotique dans certains modèles de Geffroy linéaires
Estimation de Yule–Walker d'un CAR(p) observé à temps discret
Estimation for misspecified ergodic diffusion processes from discrete observations
The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the...
Estimation for misspecified ergodic diffusion processes from discrete observations
The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of...
Estimation in a model with infinite-dimensional nuisance parameter.
Estimation in autoregressive model with measurement error
Consider an autoregressive model with measurement error: we observe Zi = Xi + εi, where the unobserved Xi is a stationary solution of the autoregressive equation Xi = gθ0(Xi − 1) + ξi. The regression function gθ0 is known up to a finite dimensional parameter θ0 to be estimated. The distributions of ξ1 and X0 are unknown and gθ belongs to a large class of parametric regression functions. The distribution of ε0is completely known. We propose an estimation procedure with a new criterion computed as...
Estimation in models driven by fractional brownian motion
Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ x and μ(x)=μ or μ(x)=μ x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...
Estimation of parameters of RCA with exponential marginals.
Estimation of the hazard function in a semiparametric model with covariate measurement error
We consider a failure hazard function, conditional on a time-independent covariate Z, given by . The baseline hazard function and the relative risk both belong to parametric families with . The covariate Z has an unknown density and is measured with an error through an additive error model U = Z + ε where ε is a random variable, independent from Z, with known density . We observe a n-sample (Xi, Di, Ui), i = 1, ..., n, where Xi is the minimum between the failure time and the censoring time, and...